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List of Main Symbols

a, b : amplitude of the waves.

cijkl (CIJ) : stiffnesses (Voigt notation).

D : directivity factor.

D : electric induction (displacement) vector.

E : Young modulus.

E : electric field vector.

ec (ep) : kinetic (potential) energy per unit volume.

eijk (εij) : piezoelectric (dielectric) constants.

F : force density per unit mass.

H(t) : Heaviside step function.

I : acoustic intensity.

J : Poynting vector.

K : bulk modulus.

k (k) : wave vector (number).

KM : electromechanical coupling coefficient (mode M).

l : unit vector normal to a surface.

n : unit vector of the propagation direction.

P : transported power.

pa : acoustic pressure.

p (p₀) : thermodynamic pressure (at rest).

p , q : polarization vectors.

Ps (ps) : power supplied by the source (per unit volume).

r (t) : amplitude reflection (transmission) coefficients.

R (T) : intensity reflection (transmission) coefficients.

s : entropy per unit volume.

s : phase slowness vector.

T : absolute temperature.

T : mechanical traction, stress vector.

u : mechanical displacement vector.

U : internal energy per unit volume.

v : particle velocity vector.

V^e : energy velocity vector.

V (Vg) : phase (group) velocity.

VL (VT) : velocity of longitudinal (transverse) bulk waves.

W (w) : work (per unit volume).

x : position vector.

X, Y, Z : crystallographic axes.

Ze (Y) : electrical impedance (admittance).

acoustic (mechanical) impedance.

α : attenuation coefficient.

: elastic (piezoelectric) Christoffel tensor.

δij : Kronecker’s symbol.

δ(t) : Dirac function.

: linearized strain tensor (piezoelectric solid).

η : viscosity coefficient.

θi,r,t : angle of incidence, reflection, transmission.

Θ : dilatation.

κ : bulk wave velocity ratio (VT/VL).

λ, μ : Lamé constants.

ν : Poisson’s ratio.

ρ : mass density.

ρe (σe) : electric charge density per unit volume (area).

σ (σd) : effective (differential) scattering cross-section.

σ : Cauchy stress tensor.

ϕ (ψ) : scalar (vector) potential.

Φ : electric potential.

χ : decay factor.

ω : angular frequency.